You need to hit the biggest limiter first.
With the squat you need to address the hip, knee, ankle, and foot. All impact the squat.
Hit the hip first.
You need to work on mobility aspects so you are able to achieve correct positioning when performing the squat, deadlift, or push up. Improved mobility will allow you to perform the exercise as good as possible.
Part of the reason you are quad dominant may originate from the lack of hamstring flexibility. Your body needs to find slack in the system and found a way by loading the quads.
3 way hamstring stretch with a band is a great place to start.
If you go on the CrossFit Journal there are some real good entries that address the the above skills.
A Correlate Test for Hip Flexibility
The Position: Part 3—The Push-Up
Hip Prep
Lower-Body Maintenance
Mobilizing the Hip

And there are several others on the CFJ.
Lack of internal rotation is part of the problem with the external rotation situation.
Doing a search on the episodes will pull several episodes that address each of these movements.